Question: Solve for $x$ and $y$ using elimination. ${-3x+y = -23}$ ${-4x-y = -47}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $y$ and $-y$ cancel out. $-7x = -70$ $\dfrac{-7x}{{-7}} = \dfrac{-70}{{-7}}$ ${x = 10}$ Now that you know ${x = 10}$ , plug it back into $\thinspace {-3x+y = -23}\thinspace$ to find $y$ ${-3}{(10)}{ + y = -23}$ $-30+y = -23$ $-30{+30} + y = -23{+30}$ ${y = 7}$ You can also plug ${x = 10}$ into $\thinspace {-4x-y = -47}\thinspace$ and get the same answer for $y$ : ${-4}{(10)}{ - y = -47}$ ${y = 7}$